ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
BEZIER CURVE
MATLAB CODE :-
% Cubic Bezier curve
clc
clear
syms u
% Parameter matrix
U=[u^3,u^2,u,1]
% Bezier matrix
H=[-1,3,-3,1;3,-6,3,0;-3,3,0,0;1,0,0,0]
% Geometry matrix will vary for problem
G=[0,0;2,1;5,2;6,1]
B=U*H
u=linspace(0,1);
% Blending functions
b1=subs(B(1));
b2=subs(B(2));
b3=subs(B(3));
b4=subs(B(4));
% plot Blending functions
figure(1)
plot(u,b1)
hold on
plot(u,b2)
plot(u,b3)
plot(u,b4)
grid on
ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
hold off
%Property of basis function
a=b1+b2+b3+b4;
figure(2)
plot(u,a)
P=U*(H*G)
X=P(1)
Y=P(2)
% X coordinates of Bezier curve
Px=subs(X);
% Y coordiantes of Bezier curve
Py=subs(Y);
figure(3)
% Plotting of Bezier curve
scatter(G(:,1),G(:,2),'filled')
hold on
plot(Px,Py)
grid on
axis tight
RESULTS:-
U=
[u^3, u^2, u, 1]
H=
ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
-1 3 -3 1
3 -6 3 0
-3 3 0 0
1 0 0 0
G=
0 0
2 1
5 2
6 1
B=
[- u^3 + 3*u^2 - 3*u + 1, 3*u^3 - 6*u^2 + 3*u, - 3*u^3 + 3*u^2, u^3]
P=
[- 3*u^3 + 3*u^2 + 6*u, - 2*u^3 + 3*u]
X=
- 3*u^3 + 3*u^2 + 6*u
ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
Y=
- 2*u^3 + 3*u
GRAPHS:-
ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
HERMITE CURVE
MATLAB CODE :-
% Hermite curve with blending functions
clc
clear
syms u
% Parameter matrix
U=[u^3,u^2,u,1]
% hermite matrix
H=[2,-2,1,1;-3,3,-2,-1;0,0,1,0;1,0,0,0]
% Geometry matrix will vary for problem
G=[1,1;7,4;7,6;-1,-3]
B=U*H
u=linspace(0,1);
% Blending functions
b1=subs(B(1));
b2=subs(B(2));
b3=subs(B(3));
b4=subs(B(4));
% plot Blending functions
figure(1)
plot(u,b1)
hold on
plot(u,b2)
plot(u,b3)
ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
plot(u,b4)
grid on
hold off
P=U*(H*G)
X=P(1)
Y=P(2)
% X coordinates of Hermite curve
Px=subs(X);
% Y coordiantes of Hermite curve
Py=subs(Y);
figure(2)
% Plotting of hermite curve
plot(Px,Py)
grid on
axis tight
RESULTS:-
U=
[u^3, u^2, u, 1]
H=
2 -2 1 1
-3 3 -2 -1
0 0 1 0
ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
1 0 0 0
G=
1 1
7 4
7 6
-1 -3
B=
[2*u^3 - 3*u^2 + 1, - 2*u^3 + 3*u^2, u^3 - 2*u^2 + u, u^3 - u^2]
P=
[- 6*u^3 + 5*u^2 + 7*u + 1, - 3*u^3 + 6*u + 1]
X=
- 6*u^3 + 5*u^2 + 7*u + 1
Y=
- 3*u^3 + 6*u + 1
ANAS BEPARI
FYMTECHCCR
ROLL NO- 16031224001
>>
GRAPHS:-
